Method and apparatus for producing a central pressure waveform in an oscillometric blood pressure system

ABSTRACT

A central arterial blood pressure waveform is developed from pressure waveforms obtained from proximal and distal blood pressure cuffs on the brachial artery of an arm that are inflated to a supra-systolic pressure. The proximal and distal cuff pressure waveforms associated with at least one cardiac ejection cycle are sensed. The propagation times of a blood pressure pulse from the entry of the artery to the proximal cuff and from the proximal cuff to the distal cuff are calculated, permitting calculation of a reflection coefficient of the pressure pulse at one of the proximal and distal cuffs. Assuming a physical model of wave propagation along the artery between the aorta and the proximal and distal cuffs, an estimated pressure waveform at the opening of the artery can be determined.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a divisional of parent U.S. patentapplication Ser. No. 12/632,003, filed Dec. 7, 2009, (now U.S. Pat. No.9,433,358, issued Sep. 6, 2017), which parent application, in turn, is acontinuation-in-part of U.S. patent application Ser. No. 12/455,516,filed Jun. 3, 2009; U.S. patent application Ser. No. 11/358,283, filedFeb. 21, 2006 (now U.S. Patent Publication No. 2006/0224070-A1,published Oct. 5, 2006), and now abandoned); U.S. patent applicationSer. No. 12/157,854, filed Jun. 13, 2008 (now U.S. Patent Publication No2009/0012411-A1, published Jan. 8, 2009) and claims priority from U.S.Provisional Application Ser. No. 61/201,540, filed Dec. 11, 2008. Theinvention disclosed and claimed herein is related in subject matter tothat disclosed in U.S. Pat. No. 5,913,826, issued Jun. 22, 1999; U.S.Pat. No. 6,994,675, issued Feb. 7, 2006; and the aforementioned U.S.Patent Publication No. 2006/0224070-A1 and U.S. Patent Publication No.2009/0012411-A1, all of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

Blood pressure is the net result of stroke volume and vascularresistance or impedance. Blood pressure can increase with an increase instroke volume as occurs with exercise or with adrenaline. Blood pressurecan also increase with an increase in arterial tone, which is the usualcause of essential hypertension. Blood pressure increases withvasoconstrictors such as phenylephrine or angiotensin which raise bloodpressure solely by increasing vascular stiffness.

It would be very useful to be able to quantify the relative contributionof stroke volume and arterial stiffness to blood pressure. For example,if the oscillometrically measured blood pressure is 150/80, are thesehigh numbers due to increases in stroke volume or from arterialstiffness? The decision to treat or not to treat, and/or thedetermination of what agent to use, could vary, depending upon theresult.

Similarly, the response to the treatment to be followed can vary withthe result. For example, if a vasodilator such as an angiotensinreceptor blocker (ARB) is used, the change in vascular stiffness may bemore important to follow, rather than blood pressure alone, as arterialstiffness is the primary pathology.

In the acute care setting, a non-invasive measure would help indecision-making to diagnose and manage heart failure or sepsis withvasoactive drugs and fluid.

There is also a large group of people with normal blood pressure butincreased vascular stiffness. A non-invasive way of assessing the degreeof vasoconstriction and cardiac performance would be helpful indiagnosing and treating such patients. Other patients have unrecognizedvascular stiffness yet their blood pressure does not reach the 140/90threshold of treatment. How to treat (or not to treat) these patients isunclear. The ability to further characterize those patients who may haveso-called “pre-hypertension” into those with and without vascularstiffness could provide a way forward in therapy and prevention ofpremature vascular death.

Increasingly, there is evidence that the central, aortic blood pressureand flow waveforms contain information that can help to answer thequestions above. However, the indices commonly derived from the pressurewaveform are based on apparent morphology, rather than the underlyingphysics, there are difficulties in accurately estimating the centralpressure waveform morphology from a non-invasive measurement, and it isdifficult to measure the aortic flow waveform in a non-invasive manner.This invention addresses all of these issues.

SUMMARY OF THE INVENTION Estimation of Intra-Arterial Brachial BloodPressure Waveforms

The U.S. patent application Ser. No. 12/455,516, filed Jun. 3, 2009,referred to above, discloses the transformation of an oscillometricwaveform recorded by a cuff to an estimate of the internal (brachial)arterial waveform. The correction was previously given such that theoscillometric waveform was rescaled between systolic and diastolicpressures, and then a correction amount applied such that the correctionamount was zero at zero transmural pressure, and increased by increasingamounts as transmural pressure increases. The correction amount wasgiven as a fourth power of the transmural pressure. The correctedwaveform was then rescaled again to between systolic and diastolicpressure.

According to the present invention an alternative scaling method isprovided, based on a simplified physics model, allowing betterunderstanding and parameter identification methodologies to be employed,in order to adapt the model to specific subjects.

It is first assumed that the cuff contains a fixed (molar) amount offluid (usually air) during the measurement (as is the case duringsuprasystolic oscillometric measurement). Then the bulk modulus, K,relates the change in volume to the change in pressure, assuming thereare no dynamic effects:

$K = {- \frac{{V(0)}\left( {{p_{o}(t)} - {p_{o}(0)}} \right)}{{V(t)} - {V(0)}}}$

It is also assumed that the change in volume is completely accounted forby a change in the radius of the inner wall of the cuff, i.e. a changein outer radius of the arm. This equation is a linear approximation ofthe change in volume, where w is the width of the cuff.V(t)−V(0)=−2πwr _(o)(t)(r _(o)(t)−r _(o)(0))

One can model the soft tissue under the cuff as a thick-walled cylinder(see Benham and Crawford, eq 15.18), with the artery at the centre ofthe cylinder. This assumes there is some “effective” internal andexternal radius ratio. The actual geometry is such that the artery isquite close to one surface and far from another. Also, there is a bonein the middle, as well as other blood vessels. Again, we assume thestrain equilibrates.

$\frac{{r_{o}(t)} - {r_{o}(0)}}{r_{o}(t)} = {\frac{\sigma_{\theta}(t)}{Ey} - \frac{v\left( {{\sigma_{r}(t)} + \sigma_{z}} \right)}{Ey}}$

One may then write the equations relating stresses to pressures. Notethat we are implicitly assuming small displacements, as the unstressed(initial) inside and outside radii are used. We further assume that thecylinder has piston ends. p_(o)[t] and p_(i)[t] are used as these arethe pressures at equilibrium, not those initially applied.

σ_(r)(t) = −p_(o)(t)${\sigma_{\theta}(t)} = \frac{{2{p_{i}(t)}} - {\left( {{k(t)}^{2} + 1} \right){p_{o}(t)}}}{{k(t)}^{2} + 1}$${k(t)} = \frac{r_{o}(0)}{r_{i}(0)}$ σ_(z) = 0

From the above equations one may eliminate the time dependent variablesfor cuff volume, stresses, radius ratios, and external radius. One thensolves the equations for the internal pressure as a function of time.The result is as follows:

${p_{i}(t)} = {{- \frac{1}{2}}\left( {\frac{{r_{o}(0)}^{2}}{{r_{i}(0)}^{2}} + 1} \right)\left( {\frac{{Ey}\left( {{\sqrt{\pi}{{Kwr}_{o}(0)}} - \sqrt{{Kw}\left( {{\pi\;{{Kwr}_{o}(0)}^{2}} + {2{V(0)}\Delta\;{p_{o}(t)}}} \right)}} \right)}{\sqrt{{Kw}\left( {{\pi\;{{Kwr}_{o}(0)}^{2}} + {2{V(0)}\Delta\;{p_{o}(t)}}} \right)} + {\sqrt{\pi}{{Kwr}_{o}(0)}}} + {\left( {v - 1} \right){p_{o}(t)}}} \right)}$

This form of the equation permits identification of some special cases,which may be used to estimate the parameters to the model.

When Δp_(o)[t]=0, i.e. when cuff pressure is at the mean cuff pressurep_(o)[t]. For example, when cuff pressure is set to diastolic pressure,we can assume no pressure augmentation in the artery, so assuming wehave measured mean pressure non-invasively, then we knowp_(i)[t_(mean)], p_(o)[t_(mean)]==DBP and can thus find the radiusratio. We can also further assume incompressibility of the soft tissue,in which case ν→0.5. Solving for radius ratio, k, gives:

$k^{2} = {\frac{4{p_{i}(t)}}{p_{o}(t)} - 1}$

When p_(i)[t]==p_(o)[t], so, for example, when cuff pressure is set tobetween DBP and SBP, the external radius is dependent on V[0] andΔp_(o)[t] (i.e. pressure fluctuations in the cuff). We again assumeincompressibility. Solving for external radius gives:

${r_{o}(0)}^{2} = {- \frac{{V(0)}\Delta\;{p_{o}(t)}\left( {{2{{Ey}\left( {k^{2} + 1} \right)}} + {\left( {k^{2} - 3} \right){p_{o}(t)}}} \right)^{2}}{4\pi\;{{Ey}\left( {k^{4} - {2k^{2}} - 3} \right)}{{Kwp}_{o}(t)}}}$

One can also get an idea of the form of the relationship betweeninternal pressure and Δpo[t] by rearranging and simplifying:

${p_{i}(t)} = {{- \frac{1}{2}}\left( {\frac{{r_{o}(0)}^{2}}{{r_{i}(0)}^{2}} + 1} \right)\left( {{{Ey}\left( {\frac{2}{\sqrt{\frac{2{V(0)}\Delta\;{p_{o}(t)}}{\pi\;{{Kwr}_{o}(0)}^{2}} + 1} + 1} - 1} \right)} + {\left( {v - 1} \right){p_{o}(t)}}} \right)}$

It is apparent that this expression takes the form:p _(i) =c ₁ /f(Δp _(o))+c ₂  i.

where c₁ and c₂ are constant relative to Δp_(o) and p_(i), and f is apower function.

FIG. 4 is a plot of this relationship, ignoring any linear scaling andoffset. Using the following physiological values for the variables

$\quad\left\{ {{k->\sqrt{\frac{7}{5}}},{{Ey}->{50\mspace{14mu}{Kilo}\mspace{14mu}{Pascal}}},{K->{10.1\mspace{14mu}{Pascal}}},{v->0.5},{w->{120\mspace{14mu}{Meter}\mspace{14mu}{Milli}}},{{r_{o}(0)}->{6\mspace{14mu}{Centi}\mspace{14mu}{Meter}}},{{V(0)}->{100\mspace{14mu}{Liter}\mspace{14mu}{Milli}}},{{p_{o}(t)}->{{150\mspace{14mu}{MillimeterMercury}} + {133.322\mspace{14mu}{Pascal}\mspace{14mu} x}}},{{\Delta\;{p_{o}(t)}}->{133.322\mspace{14mu}{Pascal}\mspace{14mu} x}}} \right\}$

results in the plot of FIG. 5. These plots indicate that c₁, c₂ and fshould be chosen such that increments in Δp_(o) at larger values ofΔp_(o) result in smaller increments in p_(i) than equal increments inΔp_(o) at smaller values of Δp_(o).

Note that the value for bulk modulus, K, is much less than that of air(normally 10⁵ Pa) which corresponds to the fact that the cuff is veryconformable and changes in pressure cause changes in volume due to shapechanges, rather than compression of the air inside.

It may also be observed that a naïve use of this model does notcorrectly predict the relationship for subdiastolic cuff pressures. Thisis probably due to changes in the effective radius ratio for an arteryundergoing collapse.

The above model has implications in the design of the waveform sensingcuff device. In particular, the relationship between arterial and cuffpressure oscillation becomes more linear if any of the following occur:

Bulk modulus increases

Cuff internal radius increases

Volume contained in the cuff decreases

The amplitude of the pressure oscillations for any given arterial pulsepressure is predicted to increase if any of the following occur:

Bulk modulus increases

Cuff width increases

Cuff internal radius increases

Volume of cuff decreases

Determining Parameters of Aortic-Brachial Model

The U.S. patent application Ser. No. 12/455,516, filed Jun. 3, 2009,referred to above, discloses a method for reconstructing the centralaortic pressure waveform from a suprasystolic, upper-arm, oscillometricsignal. The method made use of a model with two parameters,corresponding to a reflection coefficient and the propagation time delayalong the subclavian-axillary artery.

This previous application mentioned the potential to identify theseparameters from additional measurements, for example, the use of aheart-sounds sensor to estimate the entry of a pressure pulse into thesubclavian artery.

The present invention provides additional methods for the determinationof parameters to the model of wave propagation between the aorta and thecuff.

As already discussed, a heart sounds sensor could be employed. Thisdetects the time of the valve closure. By estimating the systolicduration from the brachial waveform, we may estimate the start ofsystole.

A tonometer of some sort may be applied to the subclavian or carotidartery. This would allow detection of the onset of the pressure wave asit passed the location of the tonometer, which would be close to thestart of the subclavian artery.

An ECG may be used to determine the R-wave, which corresponds todepolarization of the cardiac muscle in preparation for the ejectionphase.

The above methods allow estimation of the time delay parameter.Disclosed below is another method using a system of two (or more) cuffs(one more proximal to the heart) that allows the estimation of timedelay or reflection coefficient.

The relationship between central pressure, p_(t0) and pressure at theproximal cuff p_(t3) is given by

${p_{t\; 0}(t)} = {\frac{{bp}_{t\; 3}\left( {t - {dt}} \right)}{b + 1} + \frac{p_{t\; 3}\left( {{dt} + t} \right)}{b + 1}}$

One may write a similar equation for the pressure at the distal cuffp_(t4), where the additional propagation delay from the proximal to thedistal cuff is given by δt.

${p_{t\; 0}(t)} = {\frac{{bp}_{t\; 4}\left( {{- {dt}} + t - {\delta\; t}} \right)}{b + 1} + \frac{p_{t\; 4}\left( {{dt} + t + {\delta\; t}} \right)}{b + 1}}$

In the time domain, one may solve the above equations for the reflectionratio directly:

$b->\frac{{p_{t\; 4}\left( {{dt} + t + {\delta\; t}} \right)} - {p_{t\; 3}\left( {{dt} + t} \right)}}{{p_{t\; 3}\left( {t - {dt}} \right)} - {p_{t\; 4}\left( {{- {dt}} + t - {\delta\; t}} \right)}}$

δt may be estimated by another method, for example, one of the methodsgiven above.

In the complex frequency (Laplace) domain, one may write the originalequations as:

${P_{t\; 0}(s)} = {\frac{b\;{\mathbb{e}}^{- {dts}}{P_{t\; 3}(s)}}{b + 1} + \frac{{\mathbb{e}}^{dts}{P_{t\; 3}(s)}}{b + 1}}$${P_{t\; 0}(s)} = {\frac{b\;{\mathbb{e}}^{s{({{- {dt}} - {\delta\; t}})}}{P_{t\; 4}(s)}}{b + 1} + \frac{{\mathbb{e}}^{s{({{dt} + {\delta\; t}})}}{P_{t\; 4}(s)}}{b + 1}}$

This makes it possible to solve the equations for the time delay (orreflection coefficient) directly, to obtain the following result:

${\mathbb{e}}^{2{dts}} = \frac{b\left( {{P_{t\; 3}(s)} - {{\mathbb{e}}^{{- s}\;\delta\; t}{P_{t\; 4}(s)}}} \right)}{{{\mathbb{e}}^{s\;\delta\; t}{P_{t\; 4}(s)}} - {P_{t\; 3}(s)}}$

It can be seen that either the time delay or the reflection coefficientmay be easily determined in the frequency domain. Furthermore, if morethan two cuffs are used, then both parameters may be determined from thecuff assembly applied to the upper arm without resorting to heart soundssensors, tonometers or other sensor types placed elsewhere on the body.

Estimation of Forward and Backward Propagating Components

Various ones of the prior patent applications, referred to above,disclose methods to reconstruct an estimate of the central pressurewaveform from a peripheral arterial signal measured under specificconditions.

It is commonly understood that this central aortic pressure waveform(measured or estimated by whatever method) represents a superposition ofa forward going (ejection) wave down the aorta, and a reflected wavereturning from the iliac bifurcation (or thereabouts). Other proposedmodels use compliance and resistance elements to try to explain theshape of the pressure waveform. In all these cases, the estimation ofmodel parameters is either difficult or does not work well.

According to the present invention, it is possible to improve on thesemethods by recognizing that the aortic system is not time invariant. Inparticular, valve closure at the end of systole introduces a markedchange in the reflection of waves within the aorta. Specifically, priorto the valve closure, the wave reflected from the distal aorta is ableto enter the heart and due to the shape of the heart does notsignificantly reflect back into the aorta. However, once the valvecloses, the wave reflected from the distal aorta is re-reflected fromthe valve, which is a sudden change in impedance. This increases thetotal pressure within the aorta and contributes to the size of thedicrotic notch. Our research has shown that without accounting for thisadditional reflection, simulated pressure waves are morphologicallyunsatisfactory representations of measured pressure waveforms.

Accounting for this non-stationary behavior allows one to perform morecomplete analysis on central pressure waveforms, including thefollowing:

Decompose forward and reflected pressure waves

Identify dynamics of valve closure, potentially including valveinsufficiency.

Calculate the residual pressure waves (from the previous heart beat)

Estimate pressure decay due to systemic vascular resistance

Approximate the flow waveform and hence relative stroke volume.

The total, observed, central pressure waveform for any single heart beatis a superposition of the following components:

Residual pressure, caused by the static extension of the arteries withthe blood volume

Exponentially decaying pressure generated by previous heart beats(generally only the one previous is of significance)

The pressure generated by the heart in that pulse (incident wave)

The incident wave pressure reflected from the distal aorta (mostly theiliac)

The distal reflection again reflected from the aortic valve (whenclosed)

The means of calculating these components is given in the DetailedDescription of Preferred Embodiment.

Estimation of Aortic Blood Flow Waveforms

Now that we have estimated the forward and backward going components ofthe waveform, we may estimate the pressure waveform at other positionsin the aorta by merely advancing or retreating the components asappropriate, and then summing these components.

This also allows us to estimate the flow waveform, which we assume ismade up of two superimposed components (1) an ejection of volume fromthe heart, v_(Incident), and (2) an augmentation or reduction of flowdue to the pressure differential across a segment of the aorta, Δv. Forexample, if pressure downstream is higher than pressure upstream, thenthe net force acts on the volume of blood in between to impede flow.Conversely, if the proximal pressure is higher than the distal pressurethen the net force acts to enhance flow.

Stroke volume is then the integral of the flow curve found by summationof these two components over one heart beat. Vascular resistance may beestimated based on the pressure-flow relationship.

For a full understanding of the present invention, reference should nowbe made to the following detailed description of the preferredembodiments of the invention as illustrated in the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing the preferred embodiment of apparatusaccording to the invention for obtaining supra-systolic signals from ablood pressure cuff and determining from these signals certaincardiovascular medical parameters which are useful in diagnosing andtreating cardiovascular disease.

FIG. 2 is a more detailed block diagram of the apparatus of FIG. 1.

FIG. 3 is a time diagram showing a single representative aortic pressurewaveform and constituent pressure waveforms, being the incident wave andiliac reflection wave, and indicating certain cardiovascular medicalparameters which are determined according to the invention.

FIG. 4 is a graph showing the relationship between the normalizedoscillatory component of pressure in an external cuff, Δp_(o)(t), andthe normalized intra arterial pressure, p_(i)(t).

FIG. 5 is a graph showing a relationship between the oscillatorycomponent of pressure in an external cuff, Δp_(o)(t), and the intraarterial pressure, p_(i)(t), having assumed physiologically reasonablevalues for model parameters.

FIGS. 6-15 are screen shots each showing four plots illustrating theestimation of the pressure and flow waveforms from a measured pressurewaveform.

The top left chart of each screen shot shows the original (measured)pressure wave, the calculated forward and reflected pressure waveformcomponents and the estimated pressure wave found by summing thecomponent pressure waveforms.

The bottom left chart of each screen shot shows the normalized componentpressure waveforms, and the reflection coefficient associated with valveclosure.

The top right chart of each screen shot shows the estimated pressurewaveform at the original location (labeled root) and the reconstructedpressure waveform at a distance down the aorta.

The bottom right chart of each screen shot shows the estimated totalflow wave and the constituent flow waves being the incident wavegenerated by the heart, and the differential wave calculated from thedifference between the root and at distance pressure waveforms.

FIGS. 6 to 10 correspond to a first human subject given phenylephrineduring epidural anaesthesia with propofol sedation, measured at baseline(FIG. 6), after sedation (FIG. 7), soon after inflation of a tourniquet(FIG. 8), a period of time after inflation of the tourniquet (FIG. 9),and two minutes after deflation of the tourniquet (FIG. 10)

FIGS. 11 to 15 correspond to a first human subject given ephedrineduring epidural anaesthesia with propofol sedation, measured at baseline(FIG. 11), after sedation (FIG. 12), soon after inflation of atourniquet (FIG. 13), a period of time after inflation of the tourniquet(FIG. 14), and two minutes after deflation of the tourniquet (FIG. 15)

FIG. 16 is a flow chart of the steps taken to decompose a centralpressure waveform.

FIG. 17 shows the constituent waves found by decomposition of a centralpressure waveform.

FIG. 18 shows how constituent pressure waves are shifted in time toreconstruct the total pressure at a distance down the aorta.

FIG. 19 shows a preferred embodiment of sensors, including proximal anddistal cuffs and a heart sounds sensor.

FIG. 20 is a flow chart describing the steps taken to measure theinformation required to calculate parameters to a model relating aorticand brachial pressures.

FIG. 21 is a diagram showing the relationship between heart activitysensor signals and cuff oscillation signals.

FIG. 22 is a diagram showing the relationship between heart soundssensor signals and cuff oscillation signals for proximal and distalcuffs.

FIG. 23 is a block diagram of apparatus used to make measurementsrequired to calculate parameters to a model relating aortic and brachialpressures.

FIG. 24 is an overall flow diagram showing the relationship betweenvarious aspects of this invention.

FIG. 25 is a diagram showing an exponential decay fitted to thediastolic portion of a total pressure waveform.

FIG. 26 is a diagram showing incident and reflected wave components ofan aortic pressure waveform.

FIG. 27 is a diagram showing primary and secondary reflected wavecomponents of an aortic pressure waveform.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The preferred embodiments of the present invention will now be describedwith reference to FIGS. 1-27 of the drawings. Identical elements in thevarious figures are designated with the same reference numerals.

This invention concerns 1) the estimation of intra-arterial brachialblood pressure waveforms from the pressure oscillations in a brachialblood pressure cuff; 2) the estimation of parameters to a model relatingthe intra-arterial brachial blood pressure waveform to the aortic bloodpressure waveform; 3) the estimation of forward and backward propagatingcomponents of the aortic blood pressure waveform from the aortic bloodpressure waveform; and 4) the estimation of aortic blood flow waveformsfrom the forward and backward propagating components of the aortic bloodpressure waveform. The relationship between these parts of the inventionare shown in FIG. 24. FIG. 24 shows how estimation of intra-arterialbrachial blood pressure waveforms are used to estimate parametersrelating brachial and aortic blood pressure waves, which are in turnused to estimate the aortic pressure wave, which is in turn used toestimate forward and backward propagating components of the aorticpressure wave, which are in turn used to estimate the aortic blood flowwave.

Estimation of Intra-Arterial Brachial Blood Pressure Waveforms.

FIGS. 1 and 2 are block diagrams of a preferred embodiment of theoscillometric apparatus according to the invention. The apparatus iscontrolled by an embedded central processing unit (“CPU”) designated asTahoe 32. Tahoe 32 interfaces with a “great board” 34, which in turn isconnected to the other components of the apparatus. The great board 34contains custom signal processing electronics (as further explainedbelow), and is connected to cuff 16 by pneumatic connector 36. Pneumaticconnector 36 also connects NIBP measurement module 26 which controls thepneumatic pressure in cuff 16 and achieves and maintains the properpressure in cuff 16. NIBP measurement module 26 can be a commerciallyavailable unit, such as supplied by Welch Allyn under the name POEM.NIBP measurement module 26 is electronically connected to great board34, which inputs the predetermined supra-systolic pressure informationto the module 26. As shown in FIG. 1, the apparatus contains internalbatteries 38 and an external DC power supply 40, and is operated byswitch 42. The apparatus can optionally be connected to a PC 44,interfaced through the Tahoe 32.

FIG. 2 illustrates further detail of the components of the great board34. Generally, the great board 34 contains components relating to powerregulation and supply 48, an interface 50 to the Tahoe board 32, aninterface 60 to NIBP measurement module 26, and a 100 Hz generator 52for pacing A/D converter 22. Also, great board 34 comprises pneumaticinterface 54 for pneumatic connection through pneumatic connecter 36 tocuff 16. Pneumatic interface 54 is connected to pressure sensor 28within great board 34, which measures the cuff pulse waves and providesa transduced analog signal to signal conditioner (“SCON”) 56. The outputanalog signal of SCON 56 is input into A/D converter 22 where it isconverted into a digital signal and passed to the Tahoe 32. A/Dconverter 22 can be a 12 bit 16 channel A/D converter, such as AD7490.The programmer device 58 is used to load firmware into themicrocontroller 52 when the equipment is manufactured.

The Tahoe 32 comprises a dedicated CPU which performs computations onthe digitized pulse waveform signals received from the A/D converter toproduce, store and display a representative cardiac pulse waveform ofthe type shown in FIG. 3.

The Tahoe 32 then performs additional computation on the digitized pulsewaveform Δp_(o) to calculate an estimated intra-arterial blood pressurewaveform p_(i) using a relationship such as the one shown in FIG. 5.

Determining Parameters of Aortic-Brachial Model

In the preferred embodiment, measured brachial intra-arterial bloodpressure waveforms are used to estimate the pressure waveform at thesubclavian root in the aorta, p_(t0)(t). In this model, p_(t0)(t) isrelated to a proximal and distal brachial pressure as shown in FIG. 19by the formulae:p _(t0)(t)=b/(b+1)p _(t3)(t−dt)+1/(b+1)p _(t3)(t+dt)p _(t0)(t)=b/(b+1)p _(t4)(t−dt−δt)+1/(b+1)p _(t4)(t+dt+δt)

The parameters to these formulae are determined using the apparatusdescribed by the block diagram of FIG. 23. In the preferred embodiment,the measurement of signals from the proximal and distal suprasystoliccuffs is carried out according to the steps shown in FIG. 20. First bothcuffs are inflated to a suprasystolic pressure. The intra-arterialpressure waves within the brachial artery thus first impinge on theproximal cuff. Recordings of proximal cuff pressure oscillations andheart activity is made. The proximal cuff is then deflated to asubdiastolic pressure, allowing the intra-arterial pressure waves toimpinge on the distal cuff. Measurements of the distal cuff pressureoscillations and heart activity are made. Both cuffs are then fullydeflated, to prevent ischaemia.

The apparatus described is thus used to provide the following signals.The Proximal Suprasystolic Cuff provides a signal that is used toestimate the intra-arterial pressure p_(t3) and the Distal SuprasystolicCuff provides a signal that is used to estimate the intra-arterialpressure p_(t4). The Heart Activity Sensor, which is preferably a heartsounds sensor, provides a reference signal a₃ and a₄ that is common toboth proximal and distal measurements. This is shown in FIG. 22.Measurements from the Heart Activity Sensor allows the calculation ofthe propagation time δt between proximal and distal cuffs. This is alsoshown in FIG. 22. The time for a pressure wave to propagate from thesubclavian root to the proximal cuff, dt, is determined by calculatingthe difference between the time of the heart sounds and the time of thedicrotic notch on the proximal intra-arterial pressure waveform. This isillustrated in FIG. 21. The reflection coefficient b is then calculatedusing the formula

$b = \frac{{p_{t\; 4}\left( {{dt} + t + {\delta\; t}} \right)} - {p_{t\; 3}\left( {{dt} + t + {\delta\; t}} \right)}}{{p_{t\; 3}\left( {t - {dt}} \right)} - {p_{t\; 4}\left( {{- {dt}} + t - {\delta\; t}} \right)}}$

The result of these measurements and calculations is that all theparameters to the model relating brachial and aortic pressure waveformsare known and the aortic pressure waveform p_(t0)(t) can be calculated.

Estimation of Forward and Backward Propagating Components

The next step in the invention is to decompose the total aortic pressurewaveform p_(t0)(t) into estimated forward and backward travelling wavecomponents. This proceeds according to the steps shown in FIG. 16.

From the central blood pressure waveform, P, we first find the diastolicportion. From this we can calculate an exponential decay of the form:P[n+1]−P _(Res)=γ(P[n]−P _(Res))

Where n are sample indices, and γ and P_(Res) are the parameters thatfit the diastolic portion to the exponential decay curve. γ indicatesthe rate at which pressure is decaying, and P_(Res), is the steady statepressure that would be reached without subsequent heart beats.

One may thus determine the component of the waveform contributed by theprevious heart beat, assuming exponential decay of the pressure at theend of the previous beat as shown in FIG. 25.P _(Decay) [n]=γP _(Decay) [n−1];P _(Decay)[0]=P[0]-P _(Res)

One then assumes a particular form of the pressure wave generated by theheart. A suitable form, based on LV pressure waveforms, is a power of ahalf-sine wave, with a period double that of the systolic ejectionperiod (SEP), i.e:P _(Incident)=sin(πt/SEP)^(ε)0<t<SEP

The exponent ε is determined based on the slope of the observed centralpressure waveform, in order to give a reasonable approximation of theinitial gradient.

The incident wave is reflected from the distal aorta, and thisreflection can be modeled by an impedance Z_(AO) based on theapproximate geometry and material properties of the aorta. As will beseen, the absolute magnitude of the reflection wave need not be known. Asuitable reflection model can be represented as an infinite impulseresponse digital filter. One sufficient example is the following:P _(Iliac) [n]=P _(Incident) [n−δ]+γP _(Iliac) [n−1]

where δ is related to the time of the principal reflection. The incidentand reflected waves are shown diagrammatically in FIG. 26.

This reflected wave is again reflected from the aortic valve. Thisreflection only occurs when the valve is closed, i.e. the diastolicportion, as shown in FIG. 27. The reflection coefficient at the valve isthus non-stationary. A suitable approximation may be employed, such as asigmoid function with a transition at the time of the dicrotic notch.R(t)=1/(1+e ^(−σt+SEP))

Windowing the distal reflection with this sigmoid function gives thepressure waveform of the secondary reflection.P _(Valve)(t)=P _(Iliac)(t)R(t)

Once all these components (basis functions) have been identified, we mayuse principles of superposition to calculate a best-fit, P_(Est) to theoriginal central pressure waveform, P, with parameters α and β.P _(Est) =P _(Res) +αP _(Incident)+β(P _(Iliac) +P _(Valve))+P _(Decay)

An example of this curve fitting is shown in FIG. 17.

As an additional, optional step, we may refine our estimate of the shapeof the incident pressure wave by apportioning the difference betweenestimated and observed pressures to the estimate of the incidentpressure waveform and then recalculating P_(Iliac) and P_(Valve) asabove.P _(Incident)(t)←αP _(Incident)(t)−(P _(Est)(t)−P(t))α/(α+β)(1−R(t))Estimation of Aortic Blood Flow Waveforms

Now that we have estimated the forward and backward going components ofthe waveform, the total pressure waveform P_(Est,δx)(t) at a distance δxdownstream from the original position in the aorta is calculated byadvancing or retreating the components calculated previously asappropriate by a time δt, and then summing these components.P _(Est,δx)(t)=P _(Res) +αP _(Incident)(t−δt)+(P _(Iliac)(t+δt)+P_(Valve)(t−δt))+P _(Decay,δx)

The distance δx is equal to the product of wave speed and δt.

The flow waveform is then calculated as the sum of (1) an ejection ofvolume from the heart, v_(Incident), and (2) an augmentation orreduction of flow due to the pressure differential across a segment ofthe aorta, Δv.

Euler's law for incompressible flow is used to calculate Δv according tothe following:Δv(t)=υ₁(P _(Est)(t)−P _(Est,δx)(t))

υ₁ is a scaling factor related to aortic cross section. We assume thatthe flow due to ejection, V_(Incident), can be approximated by thedifference between the incident pressure wave (acting within theventricle) and the iliac reflection wave (acting outside the ventricle).v _(Incident)(t)=υ₂(P _(Incident)(t)−P _(Iliac)(t))(1−R(t))

υ₂ is another scaling factor from Euler's equation. The total flow rateis then given by:v(t)=v _(Incident)(t)+Δv(t)Medical Utility of Calculated Parameters

Various cardiovascular medical parameters which are determined by themethod and apparatus of the present invention are set forth andillustrated in FIG. 3. Those commonly known to a medical practitionerare:

Systolic pressure, p_(Sys), which is determined as the maximum of theestimated total pressure waveform, p_(t0).

Diastolic pressure, p_(Dia), which is determined as the minimum of theestimated total pressure waveform.

Mean pressure, p_(Mean), which is determined as the time-average of theestimated total pressure waveform.

Systolic ejection period, SEP, which is the time from the start of thepressure wave to the dicrotic notch.

Contractility, dP/dt_(max) (not shown) which is the maximum rate ofchange of the total pressure.

Stroke volume, SV, which is determined as the integral of the estimatedflow waveform over one heart beat.

Further cardiovascular medical parameters are made available by thisinvention which are not commonly known or measured by medicalpractitioners. They are:

Aortic incident pulse pressure, α. This is the pressure differentialgenerated by the heart during systole, and is different than the maximumpressure experienced by the arteries during systole, which would be thesystolic pressure.

Aortic reflected wave pressure, β. This is the maximum amplitude of thereflected pressure wave in the aorta, and corresponds to a force againstwhich the heart must work. It is also related to the impedance (i.e.stiffness) of the aorta.

Aortic reflected wave ratio, β/α. This is a relative measure of the sizeof the reflected pressure wave. It is similar to augmentation index, butis calculated from the wave components, not the wave morphology, andthus is a better representation of arterial stiffness. Instead of usingthe amplitudes α and β, areas under the incident and reflected wavecurves, or other measures of wave amplitude could be used.

Reserve pressure, p_(Res). This is the pressure to which the arterialsystem would trend if no further heart beats were experienced, and therewas no drainage to the venous system. That is, it is the pressure causedby the elastic arteries compressing the blood volume. It is a measure ofthe baseline elasticity and blood volume of the subject.

Decay rate, γ. This is a measure of the rate at which pressure in thearterial system dissipates. The dissipation of pressure energy primarilyoccurs is vascular resistive elements, thus decay rate is a measure ofsystemic vascular resistance.

FIGS. 6 to 15 illustrate how the cardiovascular medical parameters maybe used, with two drug therapies, to assess the cardiovascularperformance of a patient. As will be explained below, the parametersprovide useful information especially when they are determined multipletimes to generate historical data.

EXAMPLES

The following examples have been taken from knee replacement operationsby two protocols under epidural anesthesia with propofol sedation.During the operation a thigh tourniquet was applied. In the firstprotocol, the patient was given a continuous phenylephrine infusion tomaintain systolic pressure between 100 and 130 mmHg. In the secondprotocol, the patient was given ephedrine rather than phenylephrine.

Both propofol and the epidural anesthesia have a vasodilating effect,which is also expected after deflation of the thigh tourniquet.Phenylephrine is a vasoconstrictor with little effect on cardiaccontractility, whereas ephedrine acts as both a vasoconstrictor andcardiac stimulant.

The central waveform has been estimated from the suprasystolic,oscillometric waveform in each case, using the same parameters for shapecorrection, propagation delay and cuff reflection coefficient. Thescaling of oscillometric pressure to arterial pressure was the same forall cases.

A summary of the main results is as follows:

10 min 2 min After post Pre post Propofol tourni- tourni- tourni- Induc-quet quet quet Baseline tion up down down BP (mmHg) Phenyl 104/75 105/75110/73 111/72 107/70 Ephed 106/71 106/71 106/71 108/73 111/76 PR (bpm)Phenyl 88 82 55 57 74 Ephed 83 82 90 89 92 SEP (s) Phenyl 0.26 0.31 0.350.35 0.34 Ephed 0.28 0.34 0.32 0.32 0.26 dP/dt_(max) Phenyl 503 382 369334 465 (mmHg/s) Ephed 514 539 514 562 623 Incident Phenyl 28 27 26 2833 Pulse Ephed 29 31 30 32 33 Pressure (mmHg) Reflected Phenyl 23 23 5347 30 Wave Ephed 34 26 26 15 10 Ratio (%) Relative Phenyl 49 56 58 66 75SV (mL) Ephed 58 63 59 67 62 Relative Phenyl 4.4 4.6 3.2 3.8 5.6 COEphed 4.9 5.2 5.3 6 5.7 (L/min)

It can be seen that the results, calculated using the disclosures inthis invention, conform to those expected. Namely:

Systolic and diastolic pressures are roughly similar under thisprotocol.

Pulse rate decreases significantly on administration of phenylephrine,and increases slightly with ephedrine. In both cases, pulse rateincreases after the tourniquet is deflated.

Propofol anaesthesia increases systolic ejection period.

Contractility decreases markedly under the phenylephrine protocol but isstable under the ephedrine protocol. In both cases, contractilityincreased after tourniquet deflation.

Reflection ratio increased markedly with phenylephrine, but decreasedunder the ephedrine protocol (due to a combination of propofol andepidural anaesthesia)

Stroke volume increased under the phenylephrine protocol, but this isexplained by the increase in systolic ejection period and decrease inpulse rate (i.e. greater diastolic filling time). Stroke volume remainedlargely constant under the Ephedrine protocol.

Cardiac output decreased significantly under the phenylephrine protocolbut increased somewhat in response to the ephedrine protocol.

In summary, the present invention provides methods for processingpressure signals received from an inflated blood pressure cuff whichinclude:

A way of non-linearly scaling cuff pressure oscillations to create apseudo-arterial waveform. The method is based on a physical model suchthat its parameters may be determined from particular cuffconfigurations. The model may also be used to help guide and optimizecuff designs.

A way of using a proximal and distal cuff for suprasystolic measurementin a manner that allows calculation of parameters for a model to moreaccurately estimate the central pressure waveform. The method may beaugmented by or augment other sensing techniques such as tonometers, ECGor heart sounds sensors to more completely or accurately define themodel parameters. The method may operate in either the time or frequencydomains to calculate such parameters. More than two cuffs may beemployed.

A way of decomposing a central pressure waveform into incident andreflected components, based on a non-stationary model of the aorticvalve reflection coefficient and its effect on the dicrotic notch. Themethod allows the calculation of incident, distal aortic reflection,aortic valve reflection, previous beat decay and residual pressures.From these components, physiologically meaningful parameters may becalculated such as incident wave height and a true reflection ratio, asopposed to the morphology-driven (and confounded) augmentation indexparameters.

A way of utilizing the above pressure wave components to reconstruct thetotal pressure waveform at various points in the aorta and the leftventricle, and using these pressure gradients in conjunction withEuler's equations for incompressible fluids to estimate blood flow,including the flow waveform, stroke volume and cardiac output. Furthervascular parameters may then be calculated including systemicresistance.

There has thus been shown and described a novel method and apparatus forproducing a central pressure waveform in an oscillometric blood pressuresystem which fulfills all the objects and advantages sought therefor.Many changes, modifications, variations and other uses and applicationsof the subject invention will, however, become apparent to those skilledin the art after considering this specification and the accompanyingdrawings which disclose the preferred embodiments thereof. All suchchanges, modifications, variations and other uses and applications whichdo not depart from the spirit and scope of the invention are deemed tobe covered by the invention, which is to be limited only by the claimswhich follow.

What is claimed is:
 1. A method for estimating forward and reflectedcomponents of the aortic blood pressure waveform from an aortic pressurewaveform obtained from a blood pressure cuff, said method comprising thesteps of: a. inflating a blood pressure cuff on a brachial artery of anarm to a pressure at least as great as the diastolic pressure; b.holding the molar amount of fluid in the blood pressure cuff constant;c. sensing a sequence of cuff pressure waveforms associated with thebrachial artery that result from at least one cardiac ejection cycle; d.determining the portion of the aortic pressure waveform, P, that occursduring diastole; e. finding two parameters, γ and P_(Res) fitting anexponential decay to the diastolic portion of the waveform P, todetermine an exponentially decaying pressure, P_(Decay); f. assuming aform of the incident waveform emanating from the heart, P_(Incident); g.calculating a reflected wave, P_(Iliac), from P_(Incident) and apredetermined model of reflection from the distal aorta; h. calculatinga pressure wave P_(Valve) representing a further reflection of thereflected wave P_(Iliac) from the aortic valve, wherein the furtherreflection substantially only occurs during diastole; i. calculating theparameters, α and β, that best fit an equation of the formP_(Est)=P_(Res)+α P_(Incident)+β(P_(Iliac)+P_(Valve))+P_(Decay) to themeasured aortic pressure waveform P; and j. calculating the incidentwave according to α×P_(Incident) and the reflected wave according toβ×P_(Iliac).
 2. The method of claim 1, further comprising the step ofrefining the estimate of the shape of the incident pressure wave,P_(Incident), by adding a portion of the difference between the fitted,P_(Est), and measured, P, aortic pressure waveforms to the previouslyassumed incident wave, P_(Incident).
 3. The method of claim 1, furthercomprising the steps of: reconstructing the pressure of the waveformdownstream on the artery from said cuff; and estimating the centralblood flow waveform in the artery by determining the forces inducingblood flow.
 4. The method of claim 3, where the reconstruction of thepressure waveform downstream comprises the steps of: shifting theincident pressure waveform P_(Incident) backwards in time by apredetermined amount; shifting the reflected pressure waveform P_(Iliac)forwards in time by said predetermined amount; shifting the secondaryreflected pressure waveform P_(Valve) backwards in time by saidpredetermined amount; and summing the incident, reflected, secondaryreflected, reserve and decay pressures to reconstruct the downstreampressure waveform.
 5. The method of claim 3, where the estimation of thecentral blood flow waveform comprises the steps of: calculating the flowgenerated by the heart as the product of a predetermined factor and thedifference between the incident and reflection pressure waves;calculating the flow generated by the pressure gradient as the productof a predetermined factor and the difference between the aortic pressurewaveform and the downstream pressure waveform; and summing thecalculated flows generated by the heart and pressure gradient toestimate the central blood flow waveform.